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The Best Math Tricks

Updated on August 25, 2011

Techniques You Can Use To Perform Math Quickly

Yes, that's right, here are quick-to-learn methods...ones that take only a minute to learn, that you can pick up and remember for the rest of your life. By reading only a few paragraphs of this article, you'll be amazed at what you can do.

Most of us want to run to a calculator. Many of us hate math. So what do you do when your options are limited?

Well, here's an additional option. Learn some techniques that make math easy.

The purpose of this article is to provide easy and quick techniques of mathematics. This means addition, subtraction, multiplication, and division.

Quickly Add A Consecutive List of Numbers

Example: Add all numbers from 1 to 20.

Note: This is also known as the summation of a series of numbers.

  1. Add the first and last number.

  2. Divide result by 2.

  3. Multiply result by the total of numbers in the list.

Applied Example: Add all numbers from 4 to 10.

  1. 4 + 10 = 14.

  2. 14 / 2 = 7.

  3. 7 X 7 = 49 (Since 4 to 10 involves 7 numbers).

Squaring A Number That Ends In 5 -- Super FAST!

Takes Less That 10 Seconds.

  1. Multiply the first digit of the number by itself plus 1.

  2. Insert the number "25" to the end of the result.

Example 1: The Square of 15.

  1. The first digit of 15 is "1", therefore multiply 1 X (1 + 1), or 1 X 2. The result is 2.

  2. Insert "25" at the end of the number. In this case, the result becomes 2...25, or "225".

Example 2: The Square of 45.
  1. The first digit is "4", therefore 4 X 5 = 20.
  2. Insert "25" at the end of "20" to arrive at "2025".

Multiplying by 9 Without Trying

Surprisingly Sneakiness By Using 10.

When you multiply a number by 9, all you have to do is figet the numbers and you'll quickly resolve the problem. Do the following:

  1. Multiply the number by 10.
  2. Subtract the original number from your result; this will be your answer.
Example: Multiply 28 X 9.
  1. 28 X 10 = 280.
  2. 280 - 28 = 252. This is the answer.

Testing for Divisibility -- 2

Can The Number Be Divided Evenly.

Sometimes, were are interested in finding out how to divide something up equally, with nothing left over. Using the following methods, you can quickly determine this.

Divisible by 2

If the number is even, it is divisible by 2. Most people already know this and apply this method.

Testing For Divisibility -- 3, 6, or 9

Divisible by 3

  1. Add the digits of the number together.

  2. If the result is divisible by 3, then the original number is divisible by 3.

Example: Using the number 1,284, we add 1 + 2 + 8 + 4 = 15. Since 15 is divisible by 3, the number 1,284 is also divisible by 3. (p.s. 1,284/3 = 428).

Special Note: You can also cast out numbers automatically divisible by 3 (3, 6, and 9) to make this quicker when checking large numbers.

Example: Using the number 3, 465, 899, 622. Cast out 3, 6, 9, 9, and 6, then add 4 + 5 + 8 + 2 + 2 = 21. So this number is divisible by 3.

Divisible by 6

  1. First observe if the number is an even number.

  2. If the number is even, test it for divisibility by 3.

  3. If the number is even and divisible by 3, it is divisible by 6.

Example: Above, we learned 3, 465, 899, 622 is divisible by 3. We can also see it is an even number. Therefore, it is divisible by 6.

Divisible by 9

  1. Sum the digits of the number.

  2. If the result is divisible by 9, the original number is also divisible by 9.

Example: Using the number 162, we have 1 + 6 + 2 = 9. Since 9 is divisible by 9, 162 is also divisible by 9.

Special Note: You can cast the "9"s out of a number to perform this calculation quicker. For example, 9,998,199 would be 8 + 1 = 9, and is therefore divisible by 9.

Testing For Divisibility -- 4 or 8

Divisible by 4

  1. Look at the last two digits of the number.

  2. If the result is divisible by 4, or is "00", then the number is divisible by 4.

Example1: Using the number 425,300. Since the last two digits are "00", this number is divisible by 4.

Example 2: Using the number 316. Since the last two digits are "16", this number is divisible by 4.

Divisible by 8

  1. Look at the last three digits of the number.

  2. If the result is "000" or a number evenly divisible by 8, then the original number also divides evenly by 8.

Example 1: 425,000 is evenly divisible by 8 because it ends with "000".

Example 2: The number 425,512 is evenly divisible by 8 because "512" is divisible by 8.

An Alternate Technique for 4 and 8

An additional technique that reduces their calculations is by dividing the number in half, two times in a row:

  1. If number divides evenly, two times in a row, it is divisible by 4 (and, simultaneously, you have the result).
  2. If each result is an even number, then the original number is also divisible by 8.
Example 1, Divisible by 4: Using the number 36.
  1. 36 divided by 2 is 18.
  2. 18 divided by 2 is 9. Therefore 36 is divisible by 4 (and the answer is 9).
Example 2, Divisible by 8, Using the previous number of "512".
  1. 512 divided in half is 256 (an even number).
  2. 256 divided in half is 128 (an even number).
  3. Therefore, 512 is divisible by 8.

Testing For Divisibility -- 5 or 10

Divisible by 5

If the number ends in a 5 or 0, it is divisible by 5.

Divisible by 10

If the number has two or more digits, and ends in a zero, it is divisible by 10.

These observations are already used by most of us.

Dividing Fractions -- The Simple Way

Flip It!

Note: You will need prior knowledge of multiplying fractions to complete this technique.

To Divide a Fraction

  1. Flip the second fraction.
  2. Then multiply the fractions.

Example 1/2 ÷ 1/3

  1. Switch 1/3 to "3/1".
  2. Multiply 1/2 and 3/1.
  3. The answer is "3/2", or 1 1/2
Most students in algebra quickly learn this technique, as dividing fractions is simply the process of flipping the second fraction and multiplying.

If you know of any math tricks, really good ones, or have comments concerning any of the tricks displayed here, please give me feedback. I'll be adding additional techniques from time to time, keeping this article alive.

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    • profile image

      anonymous 4 years ago

      @Mary Crowther: very bad tricks nounsense please see fuck tricks

    • Mary Crowther profile image

      Mary Crowther 5 years ago from Havre de Grace

      Very helpful lens here! Thanks for sharing your math tricks!

    • profile image

      ratetea 6 years ago

      I love math and I think fun and elementary-level math lenses like this are a great idea.

      If you want to expand this lens or make future ones, I'd be interested in more information about why these tricks work. The first one you give, summing up a list of numbers, is particularly fun to explain because there are many different ways of thinking about it. I did a fair amount of graduate work in math and I found that thinking about really simple things like the stuff on this page often lays the foundation for really deep understanding of math that can help you do more advanced things with ease.

    • AllPurposePapoon profile image

      AllPurposePapoon 6 years ago

      Nice lense, one of my recent favorite math tricks I use with my 9 year old daughter. The trick is using your fingers for the 9's multiples. Great Lense, thumbs up.

    • BlakeCzirr profile image
      Author

      BlakeCzirr 6 years ago

      @javr: Doh! Thanks for that; I'll get it fixed quickly.

    • javr profile image

      javr 6 years ago from British Columbia, Canada

      Some children love these kinds of tricks. This lens is blessed by a Squid Angel.

    • javr profile image

      javr 6 years ago from British Columbia, Canada

      You applied example above has an error: 7 X 7 = 42 should equal 49.